Q179 / 200 · TS EAMCET 2001 · Physics

A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $3: 1$. The ratio of radii of the fragments is

  • Correct answer
    A
    $1: 3^{1 / 3}$
  • B
    $3^{1 / 3}: 4$
  • C
    $4: 1$
  • D
    $2: 1$

Solution

From law of conservation of momentum $\begin{aligned} m v=\text { constant } & \\ V \rho v & =k \\ \frac{4}{3} \pi R^3 \rho v & =k\end{aligned}$ $\left(\frac{R_1}{R_2}\right)^3=\frac{v_2}{v_1} \Rightarrow \frac{R_1}{R_2}=\left(\frac{v_2}{v_1}\right)^{1 / 3}=\left(\frac{1}{3}\right)^{1 / 3}=1: 3^{1 / 3}$

Hence, the correct answer is option: 'A'.

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